I don't see how exactly snow storms would cause allergies, so either A, they don't, or B, it's not allergies. I could be wrong, I just do not see a way they connect. Your doctor obviously knows more than I do, however, it could just be that he/she was off this time. You can go for a second opinion and without telling the doctor what the first said, see what his/her diagnosis is.
As far as your breathing problems.